Inclusive probability to record an electron in elastic electromagnetic scattering by a spin one-half hadron wave packet

The inclusive probability to record an electron in elastic electromagnetic scattering of an electron by a spin one-half hadron is obtained, the initial quantum states of the electron and the hadron being described by the density matrices of a general form. Contrary to the Rosenbluth formula for the differential cross-section for this process, the first nontrivial contribution to the inclusive probability turns out to be of order $\alpha$ and not $\alpha^2$. This contribution describes the interference between the trivial contribution to the $S$-matrix and the leading contribution to its connected part. The explicit expression for this interference terms is derived. It is shown that the same interference term arises when the electron is scattered by the classical electromagnetic field produced by the hadron electromagnetic current averaged with respect to the free evolving density matrix of the hadron, even in the case of a single hadron. The interference term describes coherent scattering of the electron by the hadron wave packet and is immune to the quantum recoil experienced by a hadron due to scattering. The effective electron mass operator is found on the mass-shell.Comment: 14 pp., 2 fig

Three-body breakup within the fully discretized Faddeev equations

A novel approach is developed to find the three-body breakup amplitudes and cross sections within the modified Faddeev equation framework. The method is based on the lattice-like discretization of the three-body continuum with a three-body stationary wave-packet basis in momentum space. The approach makes it possible to simplify drastically all the three- and few-body breakup calculations due to discrete wave-packet representations for the few-body continuum and simultaneous lattice representation for all the scattering operators entering the integral equation kernels. As a result, the few-body breakup can be treated as a particular case of multi-channel scattering in which part of the channels represents the true few-body continuum states. As an illustration for the novel approach, an accurate calculations for the three-body breakup process $n+d\to n+n+p$ with non-local and local $NN$ interactions are calculated. The results obtained reproduce nicely the benchmark calculation results using the traditional Faddeev scheme which requires much more tedious and time-consuming calculations.Comment: 17 pages, 13 figure

Nature of S\bm{S}-wave NN\bm{NN} interaction and dibaryon production at nucleonic resonance thresholds

Phase shifts and inelasticity parameters for $NN$ scattering in the partial-wave channels ${}^3S_1$--${}^3D_1$ and ${}^1S_0$ at energies $T_{\rm lab}$ from zero to about 1 GeV are described within a unified $NN$ potential model assuming the formation of isoscalar and isovector dibaryon resonances near the $NN^*(1440)$ threshold. Evidence for these near-threshold resonances is actually found in the recent WASA experiments on single- and double-pion production in $NN$ collisions. There, the excitation of the Roper resonance $N^*(1440)$ exhibits a structure in the energy dependence of the total cross section, which corresponds to the formation of dibaryon states with $I(J^\pi)=0(1^+)$ and $1(0^+)$ at the $NN^*(1440)$ threshold. These two $S$-wave dibaryon resonances may provide a new insight into the nature of the strong $NN$ interaction at low and intermediate energies.Comment: 10 pages, 8 figure